How exactly does a flip-flop store bits?

The basic idea of a flip-flop is that the outputs ($Q$ and $\bar{Q}$) ``remember'' what bits are on them, until something happens. For the simple RS flip-flop, the outputs are stable until one of the inputs goes positive. For the clocked varieties of flip-flop, outputs only change when the clock pulse comes in (or if an external set/reset bit turns on in the case that the flip-flop has those inputs). So the output stores a bit on it until something makes that bit change. A bunch of flip-flops lined up can store a bunch of bits-- that's called a register.